
\chapter*{Abbreviations}

%\chapter*{Abbreviations} %[List of Abbreviations]
\addcontentsline{toc}{chapter}{List of Abbreviations}
% \begin{thenomenclature} 
% \begin{abbreviations}{WidestAbbreviation} 
% \begin{itemize} 
\begin{tabular}{p{4.0cm} p{11cm}}2D &  Two Dimensional \\
3D &  Three Dimensional\\
WSNs &  Wireless Sensor Netoworks\\
DAC Algorithm &  Distributed Average Consensus Algorithm\\
FIR filter &  Finite Impulse Response Filter\\
FO-DAC Algorithm &  First-order Distributed Average Consensus Algorithm\\
HO-DAC Algorithm &  Higher-order Distributed Average Consensus Algorithm\\
CFO-DAC Algorithm &  Constant First Order Distributed Average Consensus
Algorithm\\
FT-DAC Algorithm &  Finite Time Distributed Average Consensus Algorithm\\
LLR  &  Log Likelihood ratio\\


\end{tabular}


\chapter*{Notations}

%\chapter*{Notations} %[List of Notations]
\addcontentsline{toc}{chapter}{List of Notations}
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% \nomgroup{A}





${\cal G}$  &  Graph associated to the network \\


$\mathcal{V}$  &  Set of nodes $\mathcal{V}=\left\{ v_{1},v_{2},...,v_{n}\right\} $
in the graph ${\cal G}$\\


$\mathcal{E}$  &  Set of edges $\mathcal{E}\subseteq\mathcal{V}\times\mathcal{V}$
in the graph ${\cal G}$\\


${\cal A}$  &  Weighted adjacency associated with graph ${\cal G}$\\


$W$  &  Weight matrix of first-order DAC algorithm \\


$w_{ij}$  &  Entry of weight matrix $W$\\


$\mathbf{H}$  &  weight matrix of higher-order DAC algorithm \\


$\lambda_{i}\left(W\right)$ &  The $i^{th}$ Eigenvalue of weight
matrix $W$\\


$S\left(W\right)$  &  Spectrum of of the matrix $W$\\


\textit{$Q$ } &  Incidence matrix associated with graph ${\cal G}$\\


$L$  &  Laplacian matrix induced by ${\cal G}$\\


$l_{ij}$  &  Entry of Laplacian matrix $L$\\


$\lambda_{i}\left(L\right)$ &  The $i^{th}$ Eigenvalue of Laplacian
matrix $L=L\left({\cal G}\right)$\\


$S\left(L\right)$  &  Spectrum of the Laplacian matrix\\


$\mathbf{x}\left(k\right)$  &  Local value vector at time index
$k$\\


$x_{i}\left(k\right)$  &  Local value of node $i$ at time index
$k$\\


$\epsilon$ &  Step length of DAC algorithms\\


$\gamma$ &  Forgetting factor of DAC algorithms\\


$\epsilon_{opt,FO}$ &  Optimal step length of first-order DAC algorithms\\


$\epsilon_{opt,SO}$ &  Optimal step length of second-order DAC algorithms\\


$\gamma_{opt,SO}$ &  Optimal forgetting factor of second-order DAC
algorithms\\


$p(\lambda)$  &  The minimal polynomial of $W$ \\


$T_{i}\left(k,D_{i}\right)$  &  Toeplitz matrix in $\mathbb{R}^{D_{i}\times D_{i}}$
at $v_{i}$ with $x_{i}\left(k\right)$ as diagonal entries.\\


$\mathbf{y}_{i}\left(k,D_{i}\right)$  &  The local value history
vector at $v_{i}$ constructed by $\left[x_{i}\left(k+1\right),x_{i}\left(k+2\right),\ldots,x_{i}\left(k+D_{i}\right)\right]^{T}$
\\


$\mathbf{h}$  &  An FIR filter that can estimate the consensus value
\\


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%\end{listofsymbols}
